1.4 “solving linear inequalities”
DESCRIPTION
1.4 “solving linear inequalities”. ex 1:. Graph x > 3. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10. ex 1:. Graph x > 3. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/1.jpg)
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Graph x > 3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 1:
![Page 3: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/3.jpg)
Graph x > 3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 1:
![Page 4: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/4.jpg)
Graph x > 3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 1:
“All real numbers greater than three”
![Page 5: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/5.jpg)
Graph x –2 ex 2:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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Graph x –2 ex 2:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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Graph x –2
“All real numbers less than or equal to negative
two”
ex 2:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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Solve 5x – 8 < 12ex 3:
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Solve 5x – 8 < 12 +8 +8
ex 3:
![Page 10: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/10.jpg)
Solve 5x – 8 < 12 +8 +85x < 20
ex 3:
![Page 11: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/11.jpg)
Solve 5x – 8 < 12 +8 +85x < 20 5 5
ex 3:
![Page 12: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/12.jpg)
Solve 5x – 8 < 12 +8 +85x < 20 5 5
ex 3:
x < 4
![Page 13: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/13.jpg)
Solve 5x – 8 < 12 +8 +85x < 20 5 5
ex 3:
x < 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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Solve 5x – 8 < 12 +8 +85x < 20 5 5
ex 3:
x < 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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Solve –3x 12 ex 4:
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Solve –3x 12 –3 –3
ex 4:
![Page 17: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/17.jpg)
Solve –3x 12 –3 –3
ex 4:
x –4
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Solve –3x 12 –3 –3
When you multiply or divide by a negative ,
the inequality sign switches direction.
ex 4:
x –4
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Solve 2x + 1 6x – 23ex 5:
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Solve 2x + 1 6x – 23
–2x –2x
ex 5:
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Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
ex 5:
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Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23
ex 5:
![Page 23: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/23.jpg)
Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23 24 4x
ex 5:
![Page 24: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/24.jpg)
Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23 24 4x 4 4
ex 5:
![Page 25: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/25.jpg)
Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23 24 4x 4 4
6 x
ex 5:
![Page 26: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/26.jpg)
Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23 24 4x 4 4
6 x
ex 5:
VARIABLES ON THE LEFT-SIDE
!
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Solve 2x + 1 6x – 23
–2x –2x 1 4x – 23
+23 +23 24 4x 4 4
6 x
ex 5:
VARIABLES ON THE LEFT-SIDE
!
x 6
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
ex 6:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
ex 6:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
Graph x < 7
ex 6:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
Graph x < 7
ex 6:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
Graph x < 7
Graph x > –5 and x < 7
ex 6:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Graph x > –5
Graph x < 7
Graph x > –5 and x < 7
ex 6:
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Two simple inequalities joined by
“and” or “or”
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x > –5 and x < 7
![Page 37: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/37.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x > –5 and x < 7
![Page 38: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/38.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x > –5 and x < 7
“All real #s that are greater than negative five and less than seven”
![Page 39: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/39.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x > –5 and x < 7
“All real #s that are greater than negative five and less than seven”
–5 < x < 7
![Page 40: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/40.jpg)
Two simple inequalities joined by
“and” or “or”
![Page 41: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/41.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x < –5 or x >7
![Page 42: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/42.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x < –5 or x >7
![Page 43: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/43.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Two simple inequalities joined by
“and” or “or” x < –5 or x >7
“All real #s that are less than negative five or greater than seven”
![Page 44: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/44.jpg)
Solve –2 3x – 8 4ex 7:
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Solve –2 3x – 8 4 +8 +8 +8
ex 7:
![Page 46: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/46.jpg)
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12
ex 7:
![Page 47: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/47.jpg)
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12 3 3 3
ex 7:
![Page 48: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/48.jpg)
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12 3 3 3
2 x 4
ex 7:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12 3 3 3
x 2 and x 4
2 x 4
ex 7:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12 3 3 3 x 2
and x 4 2 x 4
ex 7:
![Page 51: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/51.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve –2 3x – 8 4 +8 +8 +8
6 3x 12 3 3 3
“All real #s that are greater than or equal to two and less than or equal to four”
x 2 and x 4 2 x 4
ex 7:
![Page 52: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/52.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5
ex 8:
![Page 53: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/53.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
ex 8:
![Page 54: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/54.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
ex 8:
![Page 55: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/55.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
ex 8:
![Page 56: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/56.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
2 2 4 4
ex 8:
![Page 57: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/57.jpg)
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
2 2 4 4
ex 8:
x < –1 or x > 3
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
2 2 4 4
ex 8:
x < –1 or x > 3
![Page 59: 1.4 “solving linear inequalities”](https://reader037.vdocuments.net/reader037/viewer/2022110402/56812b25550346895d8f25e7/html5/thumbnails/59.jpg)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
2 2 4 4
ex 8:
x < –1 or x > 3
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve 2x + 3 < 1 or 4x – 7 > 5 2x + 3 < 1 or 4x – 7 > 5
–3 –3 +7 +7
2x < –2 or 4x > 12
2 2 4 4“All real #s that are less than negative
one or greater than three”
ex 8:
x < –1 or x > 3
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
1] Graph –2 x 5
2] Is x = 9 a solution of – x – 2 –4 ?
3] Solve 5 – 2x 27 4] Solve x + 5 < 2
SOLVE & GRAPH :5] 3x + 2 –10 or 2x – 4 –4
6] –19 3x – 4 2
13
92
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
1] Graph –2 x 5
2] Is c = 9 a solution of – x – 2 –4 ?
3] Solve 5 – 2x 27 4] Solve x + 5 < 2
SOLVE & GRAPH :5] 3x + 2 –10 or 2x – 4 –4
6] –19 3x – 4 2
YES ; –5 –4
x –11
2x<
3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
x < –4 or x > 0
x –5 and x 2
13
92